Capacity of the range of tree-indexed random walk

Tianyi Bai; Yijun Wan

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arXiv · 2004.06018

Capacity of the range of tree-indexed random walk

Tianyi Bai·Yijun Wan

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Abstract

By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions $d\ge 7$, the capacity grows linearly; and in the critical dimension $d=6$, it grows asymptotically proportional to $\frac{n}{\log n}$.

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Tianyi Bai, Yijun Wan. 2020-04-13. Capacity of the range of tree-indexed random walk. https://arxiv.org/abs/2004.06018

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